1. Field of the Invention
This invention relates generally to decimation filters and more particularly, it relates to an improved non-integer CIC decimation filter which realizes non-integer decimation by utilizing low complexity virtual upsampling so as to eliminate the need to apply corrections to the integrators in the input sample domain.
2. Description of the Prior Art
As is generally well known in the communication industry, there have been developed over the years a number of industrial standards on audio digital sample rates. For example, there exists the 44.1 kHz sample rate for consumer CD players and the 48 kHz sample rate for professional digital audio. As a result, there has arisen the need of sample-rate conversion (SRC) systems for converting a stream of digital data at a first sample rate to a stream of digital data at a different second sample rate. It is also known in the art that decimation filters are widely used when performing this function in the field of communications and multi-media systems. However, it is often desirable for the decimation filter to support variable decimation ratios. Sometimes, these decimation ratios are non-integers.
For instance, if the modulator of a delta-sigma analog-to-digital converter (ADC) is operated at one-fourth of a master clock having a frequency of 12 MHz, as in many portable applications, the output of the modulator is required to be decimated by 62.5 in order to obtain a 48 kHz sampling rate. For achieving this non-integer decimation ratio, it is known in the prior art that this can be accomplished by using a fixed integer decimation which is either proceeded or followed by a sample rate converter. However, it is further known heretofore that a more efficient way to realize the non-integer decimation ratio is to embed the sample rate conversion in the decimation filter. In sigma-delta analog/digital converters, cascaded integrator-comb (CIC) filter arrangements are generally used for decimation.
The techniques of combining the sample rate conversion with commonly used CIC filters have been explored and developed in the past. The article by D. Babic, J. Vesma, and M. Renfors, “Decimation by irrational factor using CIC filter and linear interpolation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Volume 6, 2001, pp. 3677–3680, describes a decimation filter consisting of parallel CIC (cascaded integrator-comb) branches with an integer decimation ratio which are employed to produce adjacent decimated samples. This is followed by a linear interpolation between the samples in order to realize non-integer decimation.
The structure of Babic et al. for non-integer decimation is shown in FIG. 1 and is labeled “Prior Art.” As will be noted, the input signal u(n) is divided into polyphase components by a plurality of delay lines 2 each being connected in series with a parallel CIC filter 3 having the decimation factor of M. After the integer decimation, the irrational decimation is performed by using a linear interpolation block 4 connected between some of the two signal pairs where there is a shifting by one branch under certain conditions.
Further, the article by D. Babic and M. Renfors, “Flexible down-sampling using CIC filter with non-integer delay,” in Proceedings of the IEEE International Symposium on Circuits and Systems, 2002, pp. II-285–II-288, discloses a decimator structure which only uses one CIC filter and implements interpolation between the integrator and comb sections of the CIC filter. This decimator structure is illustrated in FIG. 2 and is labeled “Prior Art.” As can be seen, the decimator structure consists of N integrator stages 5 operating at input rate Fin, polynomial interpolation filter 6, resampler and N comb stages 7 operating at output sampling rate Fout. However, the structures of FIGS. 1 and 2 suffer from the drawback that their anti-imaging performance is limited by the interpolation.
Time-variant CIC-filters have been implemented to be completely equivalent to its original linear time-invariant system consisting of the interpolator and the decimator, as discussed in M. Henker, T. Hentschel, and G. Fettweis, “Time-variant CIC-filters for sample rate conversion with arbitrary rational factors,” in Proceedings of the IEEE International Conference on Electronics, Circuits and Systems, 1999, pp. 67–70. In particular, the Henker et al. paper utilizes virtual upsampling and updates the integrator section of the CIC filter at the input rate. The structure of Henker et al. for a conventional time-variant CIC filter is depicted in FIG. 3 and has been labeled “Prior Art”. However, this method requires a mass network for applying corrections to the state variables of the integrator due to the virtual upsampling.
CIC filters consisting of a cascade of ideal integrator stages operating at a high sampling rate and an equal number of comb stages operating at a low sampling rate are discussed in E. B. Hogenauer, “An economical class of digital filters for decimation and interpolation,” IEEE Trans. Acoust. Speech, Signal Processing, vol. ASSP-29, pp. 155–162, April 1981.
Comb filter structures for decimators and interpolators in multistage, multirate digital structure filters are discussed in literature by S. Chu and C. Burrus, “Multirate filter designs using comb filters,” IEEE Trans. Circuits Syst., vol. 31, no. 11, pp. 913–924, November 1984.
Accordingly, it would be desirable to provide an improved non-integer CIC decimation filter, which eliminates the need for applying corrections to the state variables of the integrators in the input sample domain. It would also be expedient that the CIC decimation filter exhibit a much smaller gain so as to significantly reduce the word length of the datapath.